/*
- * Copyright 2014-2017 The OpenSSL Project Authors. All Rights Reserved.
+ * Copyright 2014-2018 The OpenSSL Project Authors. All Rights Reserved.
* Copyright (c) 2014, Intel Corporation. All Rights Reserved.
* Copyright (c) 2015, CloudFlare, Inc.
*
#if defined(__x86_64) || defined(__x86_64__) || \
defined(_M_AMD64) || defined(_M_X64) || \
- defined(__powerpc64__) || defined(_ARCH_PP64)
+ defined(__powerpc64__) || defined(_ARCH_PP64) || \
+ defined(__aarch64__)
/*
* Montgomery mul modulo Order(P): res = a*b*2^-256 mod Order(P)
*/
BIGNUM *x, BN_CTX *ctx)
{
/* RR = 2^512 mod ord(p256) */
- static const BN_ULONG RR[P256_LIMBS] = { TOBN(0x83244c95,0xbe79eea2),
- TOBN(0x4699799c,0x49bd6fa6),
- TOBN(0x2845b239,0x2b6bec59),
- TOBN(0x66e12d94,0xf3d95620) };
+ static const BN_ULONG RR[P256_LIMBS] = {
+ TOBN(0x83244c95,0xbe79eea2), TOBN(0x4699799c,0x49bd6fa6),
+ TOBN(0x2845b239,0x2b6bec59), TOBN(0x66e12d94,0xf3d95620)
+ };
/* The constant 1 (unlike ONE that is one in Montgomery representation) */
- static const BN_ULONG one[P256_LIMBS] = { TOBN(0,1),TOBN(0,0),
- TOBN(0,0),TOBN(0,0) };
- /* expLo - the low 128bit of the exponent we use (ord(p256) - 2),
- * split into 4bit windows */
- static const unsigned char expLo[32] = { 0xb,0xc,0xe,0x6,0xf,0xa,0xa,0xd,
- 0xa,0x7,0x1,0x7,0x9,0xe,0x8,0x4,
- 0xf,0x3,0xb,0x9,0xc,0xa,0xc,0x2,
- 0xf,0xc,0x6,0x3,0x2,0x5,0x4,0xf };
+ static const BN_ULONG one[P256_LIMBS] = {
+ TOBN(0,1), TOBN(0,0), TOBN(0,0), TOBN(0,0)
+ };
/*
* We don't use entry 0 in the table, so we omit it and address
* with -1 offset.
BN_ULONG table[15][P256_LIMBS];
BN_ULONG out[P256_LIMBS], t[P256_LIMBS];
int i, ret = 0;
+ enum {
+ i_1 = 0, i_10, i_11, i_101, i_111, i_1010, i_1111,
+ i_10101, i_101010, i_101111, i_x6, i_x8, i_x16, i_x32
+ };
/*
* Catch allocation failure early.
}
ecp_nistz256_ord_mul_mont(table[0], t, RR);
+#if 0
+ /*
+ * Original sparse-then-fixed-window algorithm, retained for reference.
+ */
for (i = 2; i < 16; i += 2) {
ecp_nistz256_ord_sqr_mont(table[i-1], table[i/2-1], 1);
ecp_nistz256_ord_mul_mont(table[i], table[i-1], table[0]);
ecp_nistz256_ord_mul_mont(out, out, t); /* ffffffff00000000ffffffffffffffff */
/*
- * The bottom 128 bit of the exponent are easier done with a table
+ * The bottom 128 bit of the exponent are processed with fixed 4-bit window
*/
for(i = 0; i < 32; i++) {
+ /* expLo - the low 128 bits of the exponent we use (ord(p256) - 2),
+ * split into nibbles */
+ static const unsigned char expLo[32] = {
+ 0xb,0xc,0xe,0x6,0xf,0xa,0xa,0xd,0xa,0x7,0x1,0x7,0x9,0xe,0x8,0x4,
+ 0xf,0x3,0xb,0x9,0xc,0xa,0xc,0x2,0xf,0xc,0x6,0x3,0x2,0x5,0x4,0xf
+ };
+
ecp_nistz256_ord_sqr_mont(out, out, 4);
/* The exponent is public, no need in constant-time access */
ecp_nistz256_ord_mul_mont(out, out, table[expLo[i]-1]);
}
+#else
+ /*
+ * https://briansmith.org/ecc-inversion-addition-chains-01#p256_scalar_inversion
+ *
+ * Even though this code path spares 12 squarings, 4.5%, and 13
+ * multiplications, 25%, on grand scale sign operation is not that
+ * much faster, not more that 2%...
+ */
+
+ /* pre-calculate powers */
+ ecp_nistz256_ord_sqr_mont(table[i_10], table[i_1], 1);
+
+ ecp_nistz256_ord_mul_mont(table[i_11], table[i_1], table[i_10]);
+
+ ecp_nistz256_ord_mul_mont(table[i_101], table[i_11], table[i_10]);
+
+ ecp_nistz256_ord_mul_mont(table[i_111], table[i_101], table[i_10]);
+
+ ecp_nistz256_ord_sqr_mont(table[i_1010], table[i_101], 1);
+
+ ecp_nistz256_ord_mul_mont(table[i_1111], table[i_1010], table[i_101]);
+
+ ecp_nistz256_ord_sqr_mont(table[i_10101], table[i_1010], 1);
+ ecp_nistz256_ord_mul_mont(table[i_10101], table[i_10101], table[i_1]);
+
+ ecp_nistz256_ord_sqr_mont(table[i_101010], table[i_10101], 1);
+
+ ecp_nistz256_ord_mul_mont(table[i_101111], table[i_101010], table[i_101]);
+
+ ecp_nistz256_ord_mul_mont(table[i_x6], table[i_101010], table[i_10101]);
+
+ ecp_nistz256_ord_sqr_mont(table[i_x8], table[i_x6], 2);
+ ecp_nistz256_ord_mul_mont(table[i_x8], table[i_x8], table[i_11]);
+
+ ecp_nistz256_ord_sqr_mont(table[i_x16], table[i_x8], 8);
+ ecp_nistz256_ord_mul_mont(table[i_x16], table[i_x16], table[i_x8]);
+
+ ecp_nistz256_ord_sqr_mont(table[i_x32], table[i_x16], 16);
+ ecp_nistz256_ord_mul_mont(table[i_x32], table[i_x32], table[i_x16]);
+
+ /* calculations */
+ ecp_nistz256_ord_sqr_mont(out, table[i_x32], 64);
+ ecp_nistz256_ord_mul_mont(out, out, table[i_x32]);
+
+ for (i = 0; i < 27; i++) {
+ static const struct { unsigned char p, i; } chain[27] = {
+ { 32, i_x32 }, { 6, i_101111 }, { 5, i_111 },
+ { 4, i_11 }, { 5, i_1111 }, { 5, i_10101 },
+ { 4, i_101 }, { 3, i_101 }, { 3, i_101 },
+ { 5, i_111 }, { 9, i_101111 }, { 6, i_1111 },
+ { 2, i_1 }, { 5, i_1 }, { 6, i_1111 },
+ { 5, i_111 }, { 4, i_111 }, { 5, i_111 },
+ { 5, i_101 }, { 3, i_11 }, { 10, i_101111 },
+ { 2, i_11 }, { 5, i_11 }, { 5, i_11 },
+ { 3, i_1 }, { 7, i_10101 }, { 6, i_1111 }
+ };
+
+ ecp_nistz256_ord_sqr_mont(out, out, chain[i].p);
+ ecp_nistz256_ord_mul_mont(out, out, table[chain[i].i]);
+ }
+#endif
ecp_nistz256_ord_mul_mont(out, out, one);
/*
0, /* keycopy */
0, /* keyfinish */
ecdh_simple_compute_key,
- ecp_nistz256_inv_mod_ord /* can be #defined-ed NULL */
+ ecp_nistz256_inv_mod_ord /* can be #define-d NULL */
};
return &ret;
projects / openssl.git / blobdiff